Let I* be an order in some semisimple rational algebra A. Then its unit group is a finitely presented group. Together with Renaud Coulangeon and my two PhD students Oliver Braun and Sebastian Schoennenbeck we apply an algorithm developed by Voronoi in 1900 in the context of reduction theory of integral lattices to conpute generators and relations of the unit group of I*. The additional data from VoronoiA's algorithm can be used to solve the word problem in these generators.